Volume 96, Number 6, December 2011
|Number of page(s)||5|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||06 December 2011|
Lévy sections vs. partial sums of heteroscedastic time series
Departamento de Física, Centro de Ciências Exatas e Tecnologia, Universidade Federal de Sergipe 49.100-000, São Cristóvão-SE, Brasil
2 Instituto de Física, Universidade Federal de Alagoas - 57.072-970, Maceió-AL, Brasil
3 Instituto de Física, Universidade de Brasília - 70.919-970, Brasilia-DF, Brasil
4 Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte 59072-970, Natal-RN, Brasil
5 Instituto Federal de Alagoas - 57160-000, Marechal Deodoro-AL, Brasil
Accepted: 3 November 2011
Weakly nonstationary processes appear in many challenging problems related to the physics of complex systems. An interesting question is how to quantify the rate of convergence to Gaussian behavior of rescaled heteroscedastic time series with stationary first moments but nonstationary multifractal long-range correlated second moments. Here we use the approach which uses a recently proposed extension of the Lévy sections theorem. We analyze statistical and multifractal properties of heteroscedastic time series and find that the Lévy sections approach provides a faster convergence to Gaussian behavior relative to the convergence of traditional partial sums of variables. We also observe that the rescaled signals retain multifractal properties even after reaching what appears to be the stable Gaussian regime.
PACS: 89.75.-k – Complex systems / 02.50.-r – Probability theory, stochastic processes, and statistics / 89.65.Gh – Economics; econophysics, financial markets, business and management
© EPLA, 2011
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